The page ≪https://aboutme.google.com/ ≫:
When I click on the lock icon beside "Birthday", it's this:
Yet when I click on the edit button, it shows:
So is the account's birth year shown or hidden to the public?
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Nobody can see your "About Me" page but you. You'd need to look at your public profile.
If you go to https://profiles.google.com/me when you're logged in, it will redirect to your "public" Google profile (whether that's Google+ or not). Visit that same URL from an incognito browser tab and you'll see what other people can see.